105042412800 has 324 divisors, whose sum is σ = 404441703484. Its totient is φ = 25856409600.

The previous prime is 105042412759. The next prime is 105042412841. The reversal of 105042412800 is 8214240501.

105042412800 is a `hidden beast` number, since 10 + 504 + 24 + 128 + 0 + 0 = 666.

It is an interprime number because it is at equal distance from previous prime (105042412759) and next prime (105042412841).

It can be written as a sum of positive squares in 6 ways, for example, as 3031163136 + 102011249664 = 55056^2 + 319392^2 .

It is a super-2 number, since 2×105042412800² (a number of 23 digits) contains 22 as substring.

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 35 ways as a sum of consecutive naturals, for example, 678660 + ... + 818940.

Almost surely, 2^105042412800 is an apocalyptic number.

105042412800 is a gapful number since it is divisible by the number (10) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 105042412800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (202220851742).

105042412800 is an abundant number, since it is smaller than the sum of its proper divisors (299399290684).

It is a pseudoperfect number, because it is the sum of a subset of its proper divisors.

105042412800 is a wasteful number, since it uses less digits than its factorization.

105042412800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 140326 (or 140304 counting only the distinct ones).

The product of its (nonzero) digits is 2560, while the sum is 27.

The spelling of 105042412800 in words is "one hundred five billion, forty-two million, four hundred twelve thousand, eight hundred".